In a clinical or observational study for HIV-related diseases, the response variable (e.g., the time to a certain clinical or lab based event, the level of a specific viral or immunological marker et al.) may be censored or truncated. We propose to investigate the following three general, closely related censored regression problems, which we encounter frequently in HIV/AIDS research. 1. Inference procedures for nonproportional hazards models for right censored data. We will develop new inference procedures for semi-parametric accelerated failure time (AFT) and quantile models. We will also study the general AFT and quantile regression with the Box-Cox-type of transformation for the failure time. 2. Model checking and evaluation for censored failure time data. We will develop model diagnostic tools for AFT, quantile and linear transformation models with censored data based on martingale residuals for checking various aspects of modeling assumptions. 3. Censored data regression with high-dimensional covariates. We will study methods for reducing mean squared error of estimation when fitting exploratory regression models with right censored data when there are large numbers of covariates, when the covariates are highly correlated, or the number of failures is smaller than commonly thought prudent. Our methods will generalize principal component regression to the proportional hazards model and partial least squares and principal components regression to AFT models for fight censored data.